This is an equation from
my paper *Quantum Mechanics near Closed Time-like Lines *which
appeared in *Physical Review ***D44**, 3197Ð3217 (1991). It is the equation for the state of a quantum
computer that is, by whatever means, provided with a method
of sending its output back
in time to interact with its input . The universality of quantum computation
ensures that the results also apply to any time-travelling
physical system, not just a computer. The self-consistency
of this equation proves the self-consistency of time travel
in quantum physics. Analysis of the equation shows that
if we had a time machine and tried to use it to enact ÔparadoxesÕ
(like going back in time to prevent our building the time
machine), we would simply go back to a universe in which
those events really happened. *U *and *U* represent the motion Ð any motion we like Ð that we would initiate
when we emerge from the time machine. ÔTrÕ represents the
operation of selecting which part of the computerÕs state
it will send through the time machine. And represents the combining
of the input information with that which has travelled
back in time.